Project Scheduling Problem With Fuzzy Activity Durations : A Novel Operational Law Based Solution Framework

In this paper, we propose a novel operational law for calculating the credibility distribution of monotone functions of independent regular fuzzy numbers to study the project scheduling problem with partially (or fully) fuzzy activity durations. In this regard, we formulate three corresponding types of fuzzy models, namely the $\alpha$-cost minimization, the credibility maximization and the time-cost trade-off models, and show that they can be converted into crisp ones, and then be efficiently solved. Specifically, for the first model, its optimal solution is represented analytically, and thus determined precisely. The second and third ones can be solved exactly for small and medium, and approximately with high accuracy within reasonable time for large scale projects. Several numerical experiments on the public instance sets from the project scheduling problem library (PSPLIB) illustrate clearly the accuracy and efficiency of our treatment